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Robust sliding mode-H ∞ control approach for a class of nonlinear systems affected by unmatched uncertainties using a poly-quadratic Lyapunov function

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Abstract

This paper proposes a robust sliding mode-H ∞ control design methodology for a class of nonlinear systems with unmatched parametric uncertainty and external disturbance. The design procedure combines the high robustness of the sliding mode control (SMC) with the H ∞ norm performance. First, based on linear matrix inequalities (LMI) technique and multiple Lyapunov functions approach, the sliding surface design problem is formulated as a H ∞ state-feedback control for a reduced uncertain nonlinear system with polytopic representation. Then, a sliding mode controller that drives the system states to the sliding surface in finite time and maintains a sliding mode is constructed. Finally, a comparative study is done to prove the effectiveness of the results.

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Authors and Affiliations

  1. Unit of research C3S, ENSIT, TUNIS University, 5 Av. Taha Hussein, BP 56, Tunis, 1008, Tunisia

    Wajdi Saad & Anis Sellami

  2. LAAS, CNRS, Toulouse university, 7 Av. Colonel Roche, F-31400, Toulouse, France

    Germain Garcia

Authors
  1. Wajdi Saad
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  2. Anis Sellami
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  3. Germain Garcia
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Correspondence to Wajdi Saad.

Additional information

Recommended by Associate Editor Young Ik Son under the direction of Editor Jun Hyun Park.

Wajdi Saad was born in Tunisia in 1987. He received his B.S degree in electrical engineering and M.S. diploma degree in automatic control, in 2010 and 2012, respectively from the High School of Sciences and Techniques of Tunis (ESSTT). Currently, he is at the unit of research C3S as Ph.D student in the High National Engineering School of Tunis (ENSIT). His research interests include robust control with sliding mode and photovoltaic systems.

Anis Sellami was born in Tunisia, in 1967. He obtained his Habilitation diploma at Sciences Faculty of Tunis in 2008, and his Ph.D in Electrical Engineering at National School of Engineers of Tunis with LAASCNRS of Toulouse in 1999, and his M.S. in Automatic Control and B.A. in Technical Sciences at Higher School in Technical Teaching, Tunis, Tunisia, in 1993 and 1990 respectively. Since December 2013, he is a professor with the Electrical Engineering Department, High National Engineering School of Tunis (ENSIT). Now, Dr. Anis Sellami is the Director of studies and Vice Director of the ENSIT. He is also member of the executive committee of Tunisian Association of the Numerical Techniques and Automatic control and Tunisian Association of Renewable Energy. His research interests include robust control with sliding mode and photovoltaic systems.

Germain Garcia received the M.S. degree in engineering, the Ph.D degree in automatic control and the Habilitation diploma (HDR), in 1984, 1988 and 1997, respectively from the National Institute of Applied Sciences (INSAT), Toulouse, France. He is currently at the LAAS-CNRS as full professor of INSAT. His research interests include robust control theory, linear matrix inequalities (LMI), constrained control and singularly perturbed models.

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Saad, W., Sellami, A. & Garcia, G. Robust sliding mode-H ∞ control approach for a class of nonlinear systems affected by unmatched uncertainties using a poly-quadratic Lyapunov function. Int. J. Control Autom. Syst. 14, 1464–1474 (2016). https://doi.org/10.1007/s12555-015-0141-9

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  • DOI: https://doi.org/10.1007/s12555-015-0141-9

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